Robotics: Forward and Inverse Kinematics

Forward Kinematics “ Finding the end effector given the joint angles”

Types of robot joints ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Robot configurations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Setting up the coordinate system: Denavit-Hartenberg Coordinates ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],x i-2 z i-1 x i-1 x i z i-2 z i Joint i Link i Link i-1 a i z i z i-1 x i , n i

Parallel or intersecting axes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Examples ,[object Object],[object Object],[object Object],[object Object], 2  1 a 1 a 2 O 2 O 1 O 0 x 1 x 0 x 2 y 1 y 2 y 0

SCARA ,[object Object],[object Object],[object Object],[object Object],z 0 x 0 z 1 x 1 x 2 z 2 x 3 x 4 z 3 z 4 i a i d i  i  i 1 a 1 0 0  1 2 a 2 0   2 3 0 d 3 0 0 4 0 d 3 0  4

Forward Kinematics ,[object Object],[object Object],[object Object]

Forward Kinematics ,[object Object],[object Object]

Relating any two link frames ,[object Object],[object Object]

Forward Kinematic computations ,[object Object],[object Object],[object Object],[object Object],[object Object]

Kinematic Calibration ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Inverse Kinmatics (IK) “ Given a goal position find the joint angles for the robot arm”

Inverse Kinematics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object], 2  1 a 1 a 2 O 2 O 1 O 0 x 1 x 0 x 2 y 1 y 2 y 0   (x,y)  2

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Workspaces ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Trajectory Planning Path Planning

Trajectory planning ,[object Object],[object Object],[object Object],[object Object]

Joint Space Trajectories ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object]

[object Object],[object Object],0 100 -20 10

Linear segments with parabolic bends ,[object Object],[object Object],[object Object],[object Object]

Ramp Up ,[object Object],[object Object]

Linear Section ,[object Object]

Robotics: Forward and Inverse Kinematics

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